Basic Math Questions and Answers

A 50 year old male purchased a 20 Year Endowment insurance policy at the age of 40 The face value of the policy was 85 000 He asks his insurance agent for a reduced paid up insurance nonforfeiture option Given the table belo and the permanent insurance amount of 48 20 per thousand determine the reduced paid up insurance value and th annual premium End of Year 7 10 15 20 Year Endowment Options Option 2 Option 1 Cash Value Reduced Paid Up Insurance Option 3 Extended Term 421 562 834 1000 Years Days 26 10 31 182 37 50 226 364 687 20 1000 Life a Annual Premium of 4 097 00 Reduced c Annual Premium of 4 625 00 Reduced

Find the original selling price 2 Elisa Carsten noticed this advertisement This week only 187 50 on all mattress sets All sets marke down 25 What is the regular selling price of a mattress set

In an experiment with animals in a petting zoo there are 4 goats 5 sheep and 3 llamas If the gate is left open what is the probability that a goat will get out be put back in and then a llama gets out To solve this problem first determine the event is The probability is 4 dependent independent

Pine Street Rector Street and Taylor Street intersect to form a triangular shaped park as show 54 Rector Street Pine Street 64 Taylor Street What is the correct order of the lengths of the streets from longest to shortest Taylor Pine Rector Pine Taylor Rector Rector Taylor Pine Rector Pine Taylor

32 Z 0 00 0 50 1 00 2 00 3 00 28 0 13 0 26 23 37 Probability 0 5000 0 6915 0 8413 09772 0 9987 138 The heights of the trees in a forest are normally distributed with a mean of 25 meters and a standard deviation of 6 meters What is the probability that a randomly selected tree in the forest has a height greater than or equal to 37 meters Use the portion of the standard normal table given to help answer the question 39 40 TIME REMAINI 01 27 30

Determine whether each triangle is congruent to A by ASA AAS or not congruent Triangle B Triangle C Triangle D Triangle E Triangle F Triangle G Triangle H Triangle I B E H Choose Choose Not Congruent Congruent by ASA Congruent by AAS Choose Choose Choose Choose Choose Choose

Customers were asked to name their favorite soft drink The results are as follows Construct a frequency distribution for the data set If needed round answers to two decimal places Coca Pepsi Dr Pepper Cola Dr Pepper Sprite Dr Pepper Mountain Coca Mountain Dew Dew Cola Sprite Pepsi Pepsi Coca Cola Dr Coca Cola Pepper Coca Cola Mountain Dew Coca Cola Coca Cola Coca Cola

Katie s Grandma is willing to give her 20 for the first time she shovels her driveway Every time after that her Grandma plans to increase that amount by 15 How much money will Katie have if she shovels the driveway 5 times Select one a 154 O b 35 O c 135 O d 24 The Griswolds spent 3 000 on clothes in 2017 If they increase the amount they spend on clothes by 5 each year How much will they spend on clothing through the year 2020 money Select one O a 13 451 O b 13 225

Select the correct answer I 2 2x 4 If no denominator equals zero which expression is equivalent to 2 16 r 3r 4 OA B r 1 2 x 4 2 x 1 OC 2 OD 2 2 x 4

A computer purchased for 1 100 loses 16 of its value every year The computer s value can be modeled by the function v t abt where v is the dollar value and t the number of years since purchase A In the exponential model a B In how many years will the computer be worth half its original value Round answer to 1 decimal place years and b

Select the correct answer from the drop down menu The manager of the customer service department of an e commerce company wants to know the average hold time for customers who call the department The department receives about 850 calls each hour The following data set shows the hold time in minutes for 10 calls picked at random 2 1 4 5 3 3 7 4 3 2 Calculate the approximate hold time for all customers who call the customer service department The approximate hold time for all customers who call the customer service department Reset Next is 3 minutes cannot be calculated from the given data is 7 minutes

Premier Bank is planning to have a new building constructed They would like the length of the building to be 40 feet longer than its width To fit their needs each floor of the building will add 12 feet to the height of the building The cost of the foundation of the building will be 10 per square foot The cost for each successive floor of the building will be 35 000 They plan to spend 1 180 000 on construction They would also like the perimeter of the building to be 3 times the height of the building Create a system of equations to model the situation above and use it to determine how many of the solutions are viable Note The bank wants the building to be as close to their specifications as possible but the solution does not need to include whole numbers in order to be considered viable OA OB O C OD There are 2 solutions and neither are viable There are 2 solutions and both are viable There is only 1 solution and it is viable There are 2 solutions and only 1 is viable

Central School is hosting a Central Has Talent show They will award various prizes for the best 3 acts in the show First place wins the most money and each subsequent place after 1st wins 50 less than the previous place Let x equal the amount of money first place wins Which of the following expressions represents the total amount of prize money Select all that apply

2 points Marissa and Tori can shovel a driveway together in 22 min If Marissa can shovel the same driveway in 70 minutes by herself how long would it take Tori by h self

University Bank pays 5 interest compounded quarterly on regular savings accounts and Rosemont Savings Bank pays 5 5 compounded semiannually Vasily and Oxana Cherchenko had 4 000 to invest for 4 years Based on the interest to be earned which bank offers the better investment

This question is designed to be answered with a calculator Water is leaking out of a tank at a rate of r t log t 2 in gallons per minute where t is the number of minutes since the tank started leaking How many gallons of water leak out of the tank between 2 and 8 minutes O 0 065 O 0 398 O 4 986 O 6 017

The cost in dollars to produce x litres of maple syrup for the Elmira Maple Syrup Festival is C x 75 x 10 where x 400 a What is the average cost of producing 625 L b The marginal cost is C x and the marginal revenue is R x Marginal cost at x litres is the expected change in cost if we were to produce one additional litre of syrup Similarly for marginal revenue What is the marginal cost at 1225 L c How much production is needed to achieve a marginal cost of 0 50 L

For the polynomial function f x 5x 25x2 125x 0625 find the zeros Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept x 5 cross x 5 touch x 5 touch

Sam purchased a new car for 17 930 The value of the car depreciated by 19 per year When he trades the car in after x years the car is wor no more than 1 900 Fill in the values of a b and cto complete the exponential Inequality of the form a b c that can be used to determine the number of years after which the car is worth no more than 1 900 0 101 VO 0 4 a b x c X S IV TC a A B P P E 9 P sin cos tan sin cos tan csc sec cot log logg in ZAN D U 00

Draw a point that belongs to the solution region of this system of inequalities y 1 5 4 y 6 Drawing Tools Select Point Click on a tool to begin drawing 10 8 6 2 8 6 2 Delete Undo 6 00 8 Res 10

3 25H 2 25C 32 The above equation is true if Thea buys H pounds of ham slices and C pounds of cheese slices at her local deli The local deli charges 3 25 per pound of ham and 2 25 per pound of cheese According to the equation how much does Thea spend in total on both han and cheese slices

The two way frequency table below shows the preferred communication method of employees at a company based on years of employment with the company 0 to 7 years 8 or more years Total OA 44 79 OB O C OR 67 19 20 48 Text Message 36 12 48 48 84 Instant Message 49 22 71 What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication Phone Call 8 19 27 Email 21 43 64 Total 114 96 210

Suppose that you needed to make a pen for some small animals You have 13 m of fencing You decide to make a circular pen because if you wish to enclose an area using a given length of fencing then a circular fence encloses a larger area than a fence of any other shape What is the radius r of the pen Express your answer in meters to four significant figures

14 Three students take equivalent stress tests Which is the highest relative score meaning which has the largest z score value a A score of 144 on a test with a mean of 128 and a standard deviation of 34 b A score of 90 on a test with a mean of 86 and a standard deviation of 18 c A score of 18 on a test with a mean of 15 and a standard deviation of 5

Brownies are cut in the shape of right triangles The longest side of each brownie is 3 inches One brownie has a leg length 1 5 inches Which statement is true A All the brownies have a leg length of 1 5 inches because corresponding parts of congruent triangles are congruent B All the brownies are isosceles right triangles with leg lengths of 1 5 inches C None of the other brownies have leg lengths of 1 5 inches D You cannot make a conclusion using congruent triangles

Directions Find the rate of change slope Then predict the next interval Miles Per Hour 468 Hours 2 OP Rate of Change Slope Miles at 10 hours Miles 70 140 210 280 BOOKMARK 88 X

A sailmaker is designing a mainsail for a newly constructed sailboat The mainsail foot is 13 feet long the luff is 10 feet long and the luff makes a 50 angle at the head with the leach Luff Head Leech Foot Part A Determine the length of the leach 5 points Part B Find the area of the mainsail 5 points

5 What is the volume of a pyramid with a height of 10 units and a rectangular base with dimensions of five units by nine units OA 55 cubic units OB 150 cubic units OC 300 cubic units OD 450 cubic units

The symbol of a simple unprefixed SI unit has been left off of each measurement in the table below Fill in the missing unit symbols the mass of a US quarter how long a typical TV ad lasts the volume of gas in a car s full gas tank the length of a car 6 5 30 50 5 0

The drawing shows a the range of a sprinkler in the arboretum If the sprinkler reaches 3 yards what is the area covered in the green sector O square yards 3 O57 square yards O TT square yards T square yards

G 0 B 1 C 1 Which of the following best describes the construction above A ray GE bisects angle FGH F H ray GE trisects angle FGH ray GE is parallel to ray GH only

Select the correct answer The depth of a pond decreases at a rate of 2 per year If the pond currently has a depth of 5 feet in approximately how many years will the depth of the pond fall below 4 feet OA 11 years OB 50 years OC 6 years OD 24 years

Question 8 of 8 Which polynomial represents the difference below 7x8 8x6 2x 9 4x 3x 3 OA 3x 5x x 2 OB 3x8 3x7 8x 2x 6 O C 11x8 11x x 2x 6 OD 3x8 3x7 8x6 2x 6

150 135 170 175 135 140 134 130 175 160 120 125 103 170 110 140 120 150 129 150 The number of calories contained in 20 randomly selected scoops of ice cream is shown above Construct a grouped frequency distribution for the data Construct the frequency distribution with five classes and let the first class begin with 103 Type your frequency distribution in the box below Note Do not worry too much about the spacing Do the best you can in the box I will figure it out

A A Which statement BEST describes Alex s construction B C f D B Alex constructed line CD parallel to line segment AB Alex constructed line CD congruent to segment AB Alex constructed line CD to be the angle bisector of segment AB Alex constructed line CD to be the perpendicular bisector of segment AE

Question 8 Quadrilateral ABCD has vertices located at A 2 4 B 6 4 and C 1 6 as shown below y 9 8 7 6 3 F 2 2 G 0 0 H 3 2 4 3 2 8 7 6 5 4 3 2 1 0 1 2 2 1 3 A 7 5 3 4 5 6 789 B X Which of the following ordered pair for D would make this quadrilateral a parallelogram Answer

16 A cylinder has a section removed in the shape of a sector with a central angle of 40 The dimensions of the cylinder are shown in the diagram G 40 117 cm What is the volume of the remaining portion of the cylinder in cubic centimeters F 104 cm H 468 cm 9 cm J T 6 5 cm 526 5 cm

8 J ASA Similarity Postulate AA Similarity Postulate SAS Similarity Theorem K SSS Similarity Theorem L Select the postulate or theorem that you can use to conclude that the triangles are similar P N M

The square pyramid shown below has a base with sides of 10 units The slant height of the pyramid is 8 units 10 The height is What is the vertical height h Round your answer to the nearest tenth 8 units

a P1 To walk from his house A to his school C Oscar has a choice of walking along the straight roads AB and BC or taking a direct shortcut AC across a field Find how much shorter his journey will be if he chooses to take the shortcut 560 m 110 b P1 The diagram shows a quadrilateral ABCD B 1200 m 9 cm 33 7 cm A C 3 marks 16 cm D a Find the perimeter of the quadrilateral 5 marks b Find the area of the quadrilateral

7 A spherical ornament is placed into a cube shaped box for shipping The surface of the ornament touches each face of the box as shown in the diagram A If the radius of the spherical ornament is 6 centimeters which measurement is closest to the remaining volume of the cube shaped box not taken up by the ornament in cubic centimeters A 1 728 cm C 823 cm 905 cm D 2 633 cm B

Julian went to the grocery store and bought bottles of soda and bottles of juice Each bottle of soda has 25 grams of sugar and each bottle of juice has 40 grams of sugar Julian purchased a total of 13 bottles of juice and soda which collectively contain 475 grams of sugar Determine the number of bottles of soda purchased and the number of bottles of juice purchased

Complete the steps to solve the equation 6x 1 6 58 Write the original equation Apply the Subtraction Property of Equality 6x 1 658 6x X Simplify your answer Apply the Division Property of Equality Simplify your answer

When Cara drives to work it takes her 30 minutes to drive 15 miles On her days off she likes to drive to her favorite donut shop It takes Cara 6 minutes to drive to The Dreamy Donut Shop at the same rate How many miles away is The Dreamy Donut Shop

1 The bicyclists were 300 miles apart at 3 p m and were headed toward each other If they met at 9 p m and one was traveling 20 miles per hour faster than the other what was the speed of each bicyclist

24 Mason is building a 3 D model of a house for a project His model consists of a triangular prism on top of a rectangular prism as shown in the diagram 5 in 8 in 14 in 9 in Which measurement best represents the total volume of Mason s model house in cubic inches F 1 218 in 3 H 1 638 in 3 G 1 323 in 3 5 040 in 3

Select the correct answer from each drop down menu Javier purchased a digital camera for 384 The value of the camera depreciates by 25 every year This situation represents exponential decay The rate of growth or decay r is equal to year It will take years for the value of the 0 75 0 25 1 25 So the value of the camera each year is a to reach 162 Reset Next times the value in the previous

There are 28 dogs and 12 cats at Oasis Pet Resort There are 19 dogs and 6 cats at Happiness Pet Hotel Choosing which two animals describes a pair of dependent events SOA OB C OD one of the dogs at Oasis Pet Resort and then a second dog from Happiness Pet Hotel one of the cats at Happiness Pet Hotel and then a second cat from Happiness Pet Hotel one of the dogs at Oasis Pet Resort and then one of the cats at Happiness Pet Hotel one of the dogs at Oasis Pet Resort and then one of the cats at Oasis Pet Resort

A particle is moving along an axis Its displacement s units at time t seconds is determined by s t t 4t 5 At t 3 seconds is the particle moving toward or away from the axis origin At t 3 seconds is the particle speeding up slowing down or neither Explain

Tessa has recently inherited 5600 which she wants to deposit into a CD account She has determined that her two best bets are an account that compounds monthly at an annual rate of 4 7 Account 1 and an account that compounds semi annually at an annual rate of 5 1 Account 2 Step 1 of 2 Which account would pay Tessa more interest Answer Keypad Keyboard Shortcuts